Internal problem ID [14176]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {-\cos \left (y\right )^{2} y^{\prime }=-\sin \left (t \right )^{2}} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 27
dsolve(sin(t)^2=cos(y(t))^2*diff(y(t),t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\operatorname {RootOf}\left (-\textit {\_Z} +2 t +4 c_{1} -\sin \left (2 t \right )-\sin \left (\textit {\_Z} \right )\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.492 (sec). Leaf size: 35
DSolve[Sin[t]^2==Cos[y[t]]^2*y'[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \text {InverseFunction}\left [2 \left (\frac {\text {$\#$1}}{2}+\frac {1}{4} \sin (2 \text {$\#$1})\right )\&\right ][t-\sin (t) \cos (t)+c_1] \]